Which statement is correct for ( \sqrt{15} ) and (3.88) on the number line?

Correct answer: ( \sqrt{15}<3.88 )

The correct answer is option B: \(\sqrt{15}<3.88\). To compare carefully, square both positive numbers. We have \(3.88^2=15.0544\), while \((\sqrt{15})^2=15\). Since both numbers are positive and \(15<15.0544\), it follows that \(\sqrt{15}<3.88\). Indeed, \(\sqrt{15}\approx3.87298\). Option A reverses the true inequality. Option B is correct because the square-root value is slightly smaller. Option C is wrong because 3.88 is not the exact square root of 15; its square is 15.0544, not 15. Option D says 3.88 is less than 3, which is plainly false because 3.88 is greater than 3. On a number line, \(\sqrt{15}\) lies just to the left of 3.88. Memory cue: for positive numbers, squaring preserves order, so close square-root comparisons can be checked by squaring.